Question

Помогите с уравнением
1/x(x-2) + 2/(x-1)^2=2

Answer 1

1/(x²-2x)+2/(x²-2x+1)=2
x≠0;x≠2;x≠1
x²-2x=a
1/a+2/(a+1)=2
2a²+2-a-1-2a=0
2a²-3a+1=0
D=9-8=1
a1=(3-1)/4=0,5⇒x²-2x=0,5
x²-2x-0,5=0
D=4+2=6
x1=(2-√6)/2 U x2=(2+√6)/2
a2=(3+1)/4=1⇒x²-2x=1
x²-2x-1=0
D=4+4=8
x3=(2-2√2)/2=1-√2 U x4=1+√2